Do you have any thoughts what that would be?
Lattice-based KEMs have a huge design space. Here are just some of the
tradeoffs I've seen:
- IND-1CCA vs IND-CCA2: If one only needs IND-1CCA, one can get
away with a much larger decryption failure rate. This allows
smaller modulus-to-noise ratios, increasing security without
needing new assumptions. IND-1CCA is provably sufficient in
some protocols, but misusing algorithms that are only IND-1CCA
allows key-recovery attacks exploiting decryption failures.
- Noise vs rounding: Using rounding without noise reduces ciphertext sizes,
at the cost of being a much less studied assumption.
- Rings vs modules vs unstructured lattices: If efficiency isn't super
important, unstructured lattices are very attractive. A simple
example of this use-case is layer 1 optical encryption of a 100Gb/s
link, where the cost of sending a 100KB message is only 8μs.
Otherwise, one can choose between rings and modules.
- NTT-friendly rings vs large Galois groups: the former allows faster
implementations at a (likely small) increase in attack surface.
- NTRU vs {R,M}LWE: the former allows for more efficient implementations
and tighter IND-CCA2 reductions, but while it is a well-studied
problem it might have more attack surface.
- Using error-correcting codes to reduce decryption failure allows even
smaller noise-to-modulus ratios, but makes it harder to determine
the decryption failure rate.
- For quotient NTRU, implicit rejection allows tighter IND-CCA2 proofs
than the T-transform does. For product NTRU and (ring, module,
or unstructured) LWE-based schemes, one must use the T-transform,
but this also means that explicit rejection is believed to be secure.
Code-based KEMs also have a large design space, if for no other
reason than that there are many different codes to choose from. Even
lattice-based hash-and-sign signatures have many possible trapdoors.
Given all of these choices, how likely is it that there is a
one-size-fits-all best algorithm? I know that explicit elliptic curve
parameters were a disaster, but also elliptic curves had a lot fewer
tradeoffs to make.